On the representation dimension of smash products

On the representation dimension of smash products

Let A be a finite dimensional algebra graded by a finite group, and let Γ be the corresponding smash product. We prove that if A is separably graded, then the representation dimension of Γ is at least the Oppermann dimension of A plus two; if A is in addition self-injective, then the representation...

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Veröffentlicht in:Advances in applied Clifford algebras 2017-09, Vol.27 (3), p.2885-2897
Hauptverfasser: Zheng, Lijing, Huang, Chonghui, Wan, Qianhong
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theoretical
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Zusammenfassung:Let A be a finite dimensional algebra graded by a finite group, and let Γ be the corresponding smash product. We prove that if A is separably graded, then the representation dimension of Γ is at least the Oppermann dimension of A plus two; if A is in addition self-injective, then the representation dimension of Γ is at least the dimension of the stable A -module category plus two.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-017-0783-1